Need some help choosing over-ear headphones, budget ~$300

Hello everyone! I've been creeping this site for a couple weeks now and have learned a huge amount about headphones and amps, but the more I learn the more impatient I get with my current setup. So now it's time to upgrade!

I listen to a lot of different music, but the bulk of it ends up being a lot of Classic Rock/Blues (Beatles, Stones, Cream, Rush, Fleetwood Mac, etc), "Modern Rock" (Rival Sons, Incubus, Arctic Monkeys, etc) and then a HUGE amount of Radiohead and Jamiroquai. There's next to zero amount of Rap or Hip Hop ever played in my life, so hopefully that narrows it down a bit... I don't have a huge budget at the moment so I think an amp is out of the question for now, but one day soon I will definitely look into picking one up. From the research I've done so far the Grado SR325is are looking like a really good set to pump out the Rock aspect of my style, but I'm kind of nervous as to how they'd be able to handle the Radiohead and Jamiroquai. Another issue is that no one around me carries them so I can't get a demo at all. I'm not stuck on those by any means either, so I'm open to suggestions.

The Grados on pretty much the entire lineup tend to be polarzing headphones. I've heard wonderful things, and less than wonderful things. I recommend looking into the Sennheiser HD598. Great headphones with excellent comfort.

Biggest issues are the very long cord and open type build. In other words these are at home cans. Other than that they are excellent all-rounders. They should work very well with all your genres. They can do no amp, but tend to sound better with one. In this case you should have about 50 dollars left over for a small porta amp. Can't really recommend anything in that regard though.